Find $ \lim_{x\to 1}h(x)$ for $h(x)=5x^3-6x^2+2x-1$.
Answer: $h$ is a polynomial function. Polynomial functions are continuous across their entire domain, and their domain is all real numbers. In other words, for any polynomial $p$ and any possible input $c$, we know that this equality holds: $\lim_{x\to c}p(x)=p(c)$ Therefore, in order to find $ \lim_{x\to 1}h(x)$, we can simply evaluate $h$ at $x=1$. $\begin{aligned} &\phantom{=}h(x) \\\\ &=5x^3-6x^2+2x-1 \\\\ &=5(1)^3-6(1)^2+2(1)-1 \gray{\text{Substitute }x=1} \\\\ &=5-6+2-1 \\\\ &=0 \end{aligned}$ In conclusion, $ \lim_{x\to 1}h(x)=0$.